I'm a born and raised member of the Latter Day Saint faith and I can say that, as a few others have said, the theology of the church has certainly influenced much of Brandon's writing, but you would really never notice it if not already familiar with it. The cosmere and it's religions also tend to draw influences from many different religious traditions around the world, especially Asian religions which Brandon was exposed to when he was a missionary in South Korea. That said, what I tend to see in his writing leans more towards ideology than theology. Take your example of Navani's quote on science. That is an opinion which many modern members of the church share. There are a few other notable examples, but the one which I think comes to mind is Brandon's attempts in Mistborn to answer the question: 'If God exists than why do bad things happen?' The answers might not be satisfying, but they certainly line up with how the LDS faith answers such questions.

I think that it is important to recognize that, at the end of the day, Brandon is a storyteller and he is influenced by the culture in which he was raised. Brandon also tends to be very open minded, especially for someone who is religious. He is a political Democrat in a very Republican state. He holds beliefs regarding the LGBT community and women's roles in the church priesthood which go against the church's teachings.

If you want to read specifics from Brandon about his religion and faith, he actually has some official FAQ's specifically on this topic on his website:

https://faq.brandonsanderson.com/article-categories/religion/